Models of solar energetic particle fluxes- the main requirem(5)

航天,航天器,航天器环境,空间辐射

ofgalacticprotonscalculatedintermsofthemodel(Nymmiketal.,1996)forsolarminimum(sunspotnum-berW=10)andsolarmaximum(W=150).TheSEPeventselectionthresholdusedintheJPL-1991model(Feynmanetal.,1993)isshowntoo.

FromFig.3itfollowsthatamong10SEPeventswiththepeak uxdetectionthresholdFadoptedintheJPL-91model(FP1proton/(cm2ssr)),themodelmakesuseofaslittleassixeventsatEP30MeV,foureventsatEP60MeV,andtwoeventsatEP100MeV.Itcanbeseenfromthisexamplethat,inthecaseofthesmall uencesizesoftheselectedevents,theselectionmethodappliedwillleadtoarti cialeliminationoftheevents,whichhavealowpeak ux,i.e.,thetime-extendedevents(gradualevents)areeliminated.

Asaresult,thedistributionfunctionswerecalculatedforallof104Monte-Carlo-simulatedSEPeventsandalsoseparatelyforeachofthethreesetsofevents,inwhichthepeakproton uxeswereaboveoneofthethreethresholdlevelsshowninFig.3.

ThecalculationresultsareshowninFig.4(thedi er-entialdistributions)andFig.5(theintegraldistribu-tions).Itisseenthattheinitialpower-lawfunctioninEq.(1)isdistortedbyeachofthethreethresholdsandcanconditionallybedescribedtobelognormal.

Fromtheabovedata,itisseenthattheeventdetec-tionthresholdsdistortthedistributionfortheU306107protons/cm2 uences.Itisobviousthat,iftheresultantdistributionsareapproximatedbyalog-normalfunctions,themean uencesizelogarithmandthestandarddeviationofthedistributionsprovetobearti cial(butarenotthecharacteristicsofthetrue

SEPeventdistribution,whichisapowerlaw),andtode-pendontheeventdetectionandselectionthresholds.3.3.Distortionofthemeanlogarithmic uencesizebyincreasingparticleenergy

Thedistortionoftherealdistributionfunction,whichispower-law,leadsunavoidablytodistortionofthemeasuredSEP uxparametersre ectedinthemodelrepresentationatE>30MeV.

Forthesamen=104Monte-Carlo-calculatedU30P106SEPeventsobtainedintermsofthedistribu-tionEq.(1),wecalculatedthemeanlog uencesÆUlogæ

PnlogðUhUi¼10

iÞ

i¼1

ð4Þ

forthedistributionsofproton uenceswithenergies

exceedingagivenlevel,whicharebothundistortedanddistortedbythreeselectionthresholdsmentionedabove.

ThecalculationresultsareshowninFig.6.Itisseenthat,asenergyincreases,themeanlog uencesareover-estimatedarti ciallyduetoeliminationofanever-increasingnumberofeventswithsmall-sizepeak uxesfromthedataset.Hence,iftheJPL-91selectioncriterionisusedatprotonenergiesP60,themeanlog uencesareoverestimatedbyfactor5.5,whichisfullycon rmedbytheJPL-1991modelparametervalueÆU60æ=8·106protons/cm2,insteadofÆU60æ=1.4·106protons/cm2calculatedbyus(seeFig.6).IfwewanttousethesamemethodsasusedinJPL-91inthecaseofP100MeVprotons,thesystematicerrorwouldreachfactor10.Iftheselectionthresholdisdecreasedtothethresholdsde nedbytheintegralgalacticprotonspec-trum,thedistortiondecreasessomewhat.Nevertheless,thefundamentalobstaclesstillprecludeusageofthelog-normaldistributionmethodindescribingthehigh-energyparticle uencesinthe

space.